MATH 323 Real Analysis: Fall 2019


Office hours: Monday are 10--11am (anlaysis only) and 1:30--2:30pm.  More to come


Because our class was given the absolute first exam slot, none of you are expected to be very far along in your projects.  This note is meant to explain what  to include in your group presentation on Tuesday morning.

The point of these presentations is NOT to show us the details of any of the proofs you are working out but to describe, in a general way, the nature of your project.  The presentations are meant to serve two purposes:  (1)  Because it is easy to get lost in the details of the various arguments, I really want you to take a step back and be able to summarize the big picture.  Why is this questions interesting and important?  Where does it fit in the overall story we have been working through all semester?  (2) I want the folks in the class who are not working on this particular project to learn something about each of these stories.  We’ve asked a lot of questions this term, and this is a time to provide some of the answers.  Think about your audience (that will be you most of the time!)  What would be useful/interesting to hear?  (Do this!)  What would be technical and confusing?  (Don’t do this!)  I am glad to help you fine tune what to include, via office hours or email.

Presentations should be about 15 minutes in length.  The fairly short time frame is meant to eliminate the temptation to dive into the weeds of a proof. Don’t do this; you don’t have time.  Instead, tell us a story.  What is the central question?  What are one or two concrete examples that illustrate the nature of your project?  What familiar theorems are related?  Add some history if you like.  Is there a key definition of a new concept that plays a major role in your work?  If so, show us that definition.   We don’t want to see gritty proofs but you can show us pretty theorems.  In other words—explain the question, give us some help in understanding the significance of the question, and then tell us the answer.  The most impressive thing you could do—and something that would be valuable to your own understanding—is to try to explain in an informal (but not imprecise!) way, why the theorem says what it does.

You can make power point slides if you like—or write on the board.  If you write on the board, you should PRACTICE, and make sure the timing works out.   OK, enough for now.   Happy to help with individual advice.  And I'll have office hours the rest of the week to help you with some of the hurdles ahead. 


Course policies

Schedule of readings/topics/presentations

Historical Moment Presentation Guidelines

Text available for download at


Due Sep 13:  Handout on infinite series from class. For this one particular assignment, I encourage you to work with a partner or two and hand in one paper. Note that the material in sections 6.1 and 2.1 may be helpful.

Due Sep 18: Exercises 1.2.3, 1.2.4, 1.2.6, 1.2.10, 1.3.3, 1.3.5a, 1.3.11, 1.4.2, 1.4.4, 1.4.7

Due Sep 24: Exercises 1.5.2, 1.5.3 (your argument for (c) can be somewhat informal), 1.5.7, 1.5.8, 1.6.4, 1.6.10

Due Sep 27: Exercises 2.2.2ab, 2.2.7, 2.2.8, 2.3.1, 2.3.2b, 2.3.10. Note that 2.3.10(c) the hypothesis should be "If (a_n) converges to a (not zero). This typo still persists in some older versions of the text.

Due Oct 4: Exercises 2.3.12, 2.4.1 (for part (a) show bounded and monotone--see example 1.2.7), 2.4.4, 2.4.10, 2.5.1, 2.5.4, 2.5.8

Due Oct 11: Exercises 2.6.1, 2.6.2, 2.6.5, 2.6.6, 2.7.1(you can pick whether you want to do a, b, or c), 2.7.4, 2.7.6, 2.7.10

Due Oct 25: First pledged problem set. Due date moved to Oct 28.

Due Nov 4: Exercises 4.2.5cd, 4.2.6, 4.3.3 (do a or b, you pick), 4.3.8, 4.4.3, 4.4.4, 4.4.7 (exercise 4.4.5 provides a useful clue for one way to do this problem), 4.4.9; finally, finish the proof you started in class of the Intermediate Value Theorem .)

Due Nov 8: Exercises 5.2.2, 5.2.4, 5.2.7ab, 5.2.8 (I'll tell you that the conjecture in (c) is false -- see if you can name a counterexample somewhere in this assignment) 5.2.11, 5.3.1a, 5.3.3, 5.3.8

Due Nov 15: Exercises 6.2.1, 6.2.3 (just answer this for the sequence g_n), 6.2.7, 6.2.11, 6.3.1, 6.3.5ab, 6.3.6, (moving 6.4.1 to next week's assignment!)

Due Nov 22: Exercises 6.4.1, 6.4.5, 6.4.9, 6.5.3, 6.5.4, 6.5.5b (you can have part (a) for free!), 6.6.1, 6.6.5ab.

Due Dec 6: Second pledged problem set. Due in class!!

Dec 10: 9--11am. Final Project Presentations.